Finite Group Databasebeta

← #28391606

Subgroups — #28391606

Order 14464.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813655C211yesmaximal, characteristic, complemented
2#20299167C211yesmaximal, characteristic
3C2×#16813610C211yesmaximal, characteristic, complemented
4C2×#16813550C211yesmaximal, characteristic, complemented
5#20298606C211yesmaximal, characteristic, complemented
6C2×#16813538C211yesmaximal, characteristic, complemented
7#339×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic
9C22×Dic226C2211yescharacteristic
10C22×D452C2211yescharacteristic
11#16813655—22no—
12#16813655—22no—
13C2×Dic452—21no—
14C2×#14268636—21no—
15C2×#14268631C2211yescharacteristic
16#16813619—21no—
17#16813610—21no—
18#16813610—22no—
19#16813610—22no—
20#16813597—22no—
21#16813592—22no—
22C2×#14268624—22no—
23#16813550—22no—
24#16813545—22no—
25#16813538—22no—
26C2×M16×C113C2211yescharacteristic
27#117×C113C2211yescharacteristic
28C2×C42×C113C2211yescharacteristic
29C23×D113D412yes—
30#14268647—21no—
31#14268647—21no—
32#14268647—21no—
33#14268647—21no—
34C2×Dic226—21no—
35C2×Dic226—21no—
36C2×Dic226—21no—
37C2×Dic226—21no—
38C2×Dic226—21no—
39C2×Dic226D411yescharacteristic
40C2×Dic226D412yescomplemented
41C2×D452—21no—
42C2×D452—21no—
43C2×D452—21no—
44C2×D452—21no—
45C2×D452—21no—
46C2×D452—21no—
47C2×D452—24no—
48C2×D452D411yescharacteristic
49C2×C22⋊D113—21no—
50C22×Dic113—21no—
51C2×C4×D113—21no—
52Dic452—24no—
53#14268636—24no—
54#14268631—21no—
55#14268631—21no—
56C2×#11744751—21no—
57#14268624—28no—
58#14268624—24no—
59C22×C4×C113—21no—
60C22×C4×C113C2311yescharacteristic
61M16×C113—21no—
62M16×C113D412yescomplemented
63C2×C8×C113—21no—
64C4⋊C4×C113D412yes—
65C22⋊C4×C113—21no—
66C42×C113—21no—
67C42×C113—21no—
68C42×C113D412yescomplemented
69C23×C113C2×D411yescharacteristic
70C22×D113—22no—
71C22×D113—22no—
72C22×D113—21no—
73C22×D113—22no—
74C22×D113—44no—
75C2×C4×C113—22no—
76C2×C4×C113—22no—
77C2×C4×C113—42no—
78C2×C4×C113C2×D411yescharacteristic
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2×D411yescharacteristic
83C2×C4×C113#4111yescharacteristic
84C22⋊D113—41no—
85C22⋊D113—41no—
86C2×Dic113—21no—
87C2×Dic113—22no—
88C2×Dic113—41no—
89C2×Dic113—41no—
90D452—21no—
91D452—21no—
92D452—41no—
93D452—41no—
94D452—41no—
95D452—41no—
96D452—84no—
97C4×D113—41no—
98C4×D113—41no—
99Dic226—22no—
100Dic226—21no—
101Dic226—22no—
102Dic226—21no—
103Dic226—41no—
104Dic226—41no—
105C8×C113—22no—
106#11744751—41no—
107C22×C113—22no—
108C22×C113#12011yescharacteristic
109C22×C113#12011yescharacteristic
110C22×C113#12111yescharacteristic
111C2×D113—44no—
112C2×D113—41no—
113C2×D113—42no—
114C2×D113—42no—
115C2×D113—44no—
116C2×D113—82no—
117C4×C113—42no—
118C4×C113—42no—
119C4×C113#12011yescharacteristic
120C4×C113#12111yescharacteristic
121C4×C113#12111yescharacteristic
122C4×C113#12711yescharacteristic
123Dic113—42no—
124Dic113—41no—
125C2×C113—21no—
126C2×C113—21no—
127C2×C113#39211yescharacteristic
128C2×C113#45512yes—
129D113—81no—
130D113—82no—
131#2004—1131nomaximal, Sylow
132C113#200411yescharacteristic, complemented, Sylow
133C2×#137—1131no—
134#535—1131no—
135C2×#124—1131no—
136C2×#104—1131no—
137#419—1131no—
138C2×#100—1131no—
139#339D11311yescharacteristic, complemented
140C2×#41—1131no—
141C22×Q8—1131no—
142C22×D4—1131no—
143#137—2262no—
144#137—2262no—
145C2×Q16—2261no—
146C2×SD16—2261no—
147C2×M16—1131no—
148C2×M16C2×D11311yescharacteristic
149#127—2261no—
150#124—2262no—
151#124—2261no—
152#124—2262no—
153#121—2262no—
154#120—2262no—
155#117C2×D11311yescharacteristic
156C2×C22⋊C4—2262no—
157C2×C42C2×D11311yescharacteristic
158#104—2262no—
159#103—2262no—
160#100—2262no—
161C24—1132no—
162#41—2261no—
163#41—2261no—
164#41—2261no—
165#41—2261no—
166C2×Q8—1131no—
167C2×Q8—1132no—
168C2×Q8—2261no—
169C2×Q8—2261no—
170C2×Q8—2261no—
171C2×Q8—2261no—
172C2×Q8—2261no—
173C2×D4—1131no—
174C2×D4—2264no—
175C2×D4—2261no—
176C2×D4—2261no—
177C2×D4—2261no—
178C2×D4—2261no—
179C2×D4—2261no—
180C2×D4—2261no—
181C2×D4—2261no—
182C22×C4—21no—
183C22×C4—2261no—
184C22×C4—2261no—
185C22×C4C22×D11311yescharacteristic
186Q16—2264no—
187SD16—2264no—
188M16—21no—
189M16—2261no—
190M16—2261no—
191M16D45212yescomplemented
192C2×C8—21no—
193C2×C8—2261no—
194C4⋊C4D45212yes—
195C22⋊C4—21no—
196C22⋊C4—2268no—
197C22⋊C4—2264no—
198C42—21no—
199C42—21no—
200C42D45212yescomplemented
201C23—4524no—
202C23—2262no—
203C23—2262no—
204C23—2262no—
205C23—2261no—
206C23D4×D11311yescharacteristic
207Q8—4521no—
208Q8—4521no—
209Q8—2262no—
210Q8—2261no—
211Q8—2262no—
212Q8—2261no—
213D4—9044no—
214D4—4521no—
215D4—4521no—
216D4—4521no—
217D4—4521no—
218D4—4521no—
219D4—4521no—
220D4—2261no—
221D4—2261no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—4521no—
226C2×C4—4521no—
227C2×C4—4521no—
228C2×C4—4521no—
229C2×C4—2262no—
230C2×C4—2261no—
231C2×C4D4×D11311yescharacteristic
232C2×C4D4×D11311yescharacteristic
233C2×C4C2×D45211yescharacteristic
234C2×C4C2×D45211yescharacteristic
235C2×C4C2×D45211yescharacteristic
236C2×C4#1426864811yescharacteristic
237C8—22no—
238C8—4521no—
239C22—22no—
240C22—9042no—
241C22—4524no—
242C22—4521no—
243C22—4522no—
244C22—4522no—
245C22—4524no—
246C22#1681359211yescharacteristic
247C22#1681359211yescharacteristic
248C22#1681359711yescharacteristic
249C4—42no—
250C4—42no—
251C4—4521no—
252C4—4522no—
253C4#1681359211yescharacteristic
254C4#1681359711yescharacteristic
255C4#1681359711yescharacteristic
256C4#1681361911yescharacteristic
257C2—21no—
258C2—21no—
259C2—9042no—
260C2—9041no—
261C2#2029850811yescharacteristic
262C2#2029877712yes—
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#339×C113C2
socleC22×C113#120
prime radical#20299167C2
hypercenter#339D113
hypocenterC113#2004
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16813655C2semidirect
3. C2×#16813610C2semidirect
4. C2×#16813550C2semidirect
5. #20298606C2semidirect
6. C2×#16813538C2semidirect
7. #339×C113C2semidirect
40. C2×Dic226D4semidirect
62. M16×C113D4semidirect
68. C42×C113D4semidirect
132. C113#2004semidirect
139. #339D113semidirect
191. M16D452semidirect
200. C42D452semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168136552
#202991672
C2×#168136102
C2×#168135502
#202986062
C2×#168135382
#339×C1132
#2004113